• 作者： 鄭芳田; 陳清華
• 作者服務機構： 國立成功大學製造工程研究所; 吳鳳工商專科學校電機工程科
• 中文摘要： 多餘自由度機械人系統的力量分佈問題與反運動學問題的一般解，已曾被用虛擬反公式及精簡公式求得。其中，精簡公式是利用高斯消去法，仍將一般解導成由一個特殊解及同質解構成。與虛擬反公式之最主要不同點在於精簡公式的同質解僅是自由變數的函數。因此，最佳化問題之規模將大大地減少，使得求解過程之計算負荷亦大規模地減少。本論文將探討虛擬反公式與精簡公式問之關係，並明確指出，虛擬反公式能以精簡公式之方式表示。
• 英文摘要： The general solutions of redundant robotic systems for Force Distribution and Redundant InverseKinematics problems have been formulated using the traditional Pseudoinverse formulation and theCompact formulation. The Compact formulation is derived by applying Gaussian elimination with partialpivoting to transform the underspecified matrix into a row-reduced echelon form; then, the general solutionis still formulated as one particular solution together with a homogeneous solution. The major differenceis that, unlike the Pseudoinverse formulation, the homogeneous solution of the Compact formulation ismerely a function of the free variables．As such，the optimization problem size is greatly reduced sothat the computational burden (especially for constrained optimization problems with inequalities) is alsogreatly reduced. In this paper, the relationship between these two formulations is investigated. It is shownthat the Pseudoinverse formulation can be converted into the Compact formulation with the free variableschosen as a function of the arbitrary vector of the Pseudoinverse formulation．
• 中文關鍵字： pseudoinverse formulation; compact formulation; Gaussian elimination with partial pivoting
• 英文關鍵字： --